Asymptotic tracking of uncertain systems with continuous control using adaptive bounding

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Robotics

Background:

• Uncertain nonlinear systems pose significant challenges in control design.
• Existing methods often require prior knowledge of uncertainty bounds, limiting their applicability.
• Robustness and adaptability are crucial for real-world system performance.

Purpose of the Study:

• To develop a robust adaptive control design for multiple-input-multiple-output (MIMO) uncertain nonlinear systems.
• To address both parametric and nonparametric uncertainties and bounded disturbances.
• To achieve asymptotic convergence of tracking errors without prior knowledge of uncertainty bounds.

Main Methods:

• Utilized approximation properties of unknown continuous nonlinearities.
• Employed an adaptive bounding technique for controller design.
• Incorporated an integral technique involving filtered tracking error.
• Ensured boundedness of parameter estimation errors.

Main Results:

• Achieved asymptotic convergence of the tracking error to zero.
• Demonstrated robustness against parametric and nonparametric uncertainties and disturbances.
• Developed a continuous control algorithm.
• Validated theoretical results through simulation.

Conclusions:

• The proposed robust adaptive control method effectively handles uncertain nonlinear MIMO systems.
• The controller achieves precise tracking performance without requiring prior bounds on uncertainties.
• The method offers a practical approach for complex control applications.